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Diketahui:

u subscript 1 equals 4 semicolon space u subscript 2 equals 6 semicolon space u subscript 3 equals 8 semicolon space u subscript 4 equals 10 semicolon space text dan  end text u subscript 5 equals 12 v subscript 1 equals 1 semicolon space v subscript 2 equals 2 semicolon space v subscript 3 equals 4 semicolon space v subscript 4 equals 5 semicolon space text dan  end text v subscript 5 equals 6 

Carilah 

e. sum from i equals 1 to 5 of open parentheses u subscript i plus v subscript i close parentheses open parentheses u subscript i minus v subscript i close parentheses 

I. Ridha

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

nilai dari sum from i equals 1 to 5 of open parentheses u subscript i plus v subscript i close parentheses open parentheses u subscript i minus v subscript i close parentheses adalah 278.space 

Pembahasan

Ingat kembali mengenai definisi dan sifat notasi sigma:

Jika m less or equal than n semicolon space a subscript i comma space b subscript i space text bilangan real; end text space m comma space n space text bilangan bulat end text, maka

  • sum from i equals m to n of a subscript i equals a subscript m plus a subscript m minus 1 end subscript plus a subscript m minus 2 end subscript plus midline horizontal ellipsis plus a subscript n
  • table attributes columnalign right center left columnspacing 0px end attributes row cell sum from i equals m to n of open parentheses a subscript i plus b subscript i close parentheses open parentheses a subscript i minus b subscript i close parentheses end cell equals cell sum from i equals m to n of a subscript i squared minus sum from i equals m to n of b subscript i squared end cell end table 

Oleh karena itu, diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell sum from i equals 1 to 5 of open parentheses u subscript i plus v subscript i close parentheses left parenthesis u subscript i minus v subscript i right parenthesis end cell equals cell sum from i equals 1 to 5 of u subscript i squared minus sum from i equals 1 to 5 of v subscript i squared end cell row blank equals cell open parentheses u subscript 1 squared plus u subscript 2 squared plus u subscript 3 squared plus u subscript 4 squared plus u subscript 5 squared close parentheses end cell row blank blank cell negative open parentheses v subscript 1 squared plus v subscript 2 squared plus v subscript 3 squared plus v subscript 4 squared plus v subscript 5 squared close parentheses end cell row blank equals cell open parentheses 4 squared plus 6 squared plus 8 squared plus 10 squared plus 12 squared close parentheses end cell row blank blank cell negative open parentheses 1 squared plus 2 squared plus 4 squared plus 5 squared plus 6 squared close parentheses end cell row blank equals cell left parenthesis 16 plus 36 plus 64 plus 100 plus 144 right parenthesis end cell row blank blank cell negative left parenthesis 1 plus 4 plus 16 plus 25 plus 36 right parenthesis end cell row blank equals cell 360 minus 82 end cell row blank equals 278 end table   

 Dengan demikian, nilai dari sum from i equals 1 to 5 of open parentheses u subscript i plus v subscript i close parentheses open parentheses u subscript i minus v subscript i close parentheses adalah 278.space 

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